Which of the following alkaline earth metal hydroxides is the least soluble in water?

Options

A. `Be(OH)_(2)`
B. `Mg(OH)_(2)`
C. `Ca(OH)_(2)`
D. `Ba(OH)_(2)`

Answer

To determine which alkaline earth metal hydroxide is the least soluble in water, we will analyze the solubility trends of the hydroxides of alkaline earth metals (Group 2 elements).

### Step-by-Step Solution:

1. **Identify the Alkaline Earth Metals**:
The alkaline earth metals include beryllium (Be), magnesium (Mg), calcium (Ca), strontium (Sr), and barium (Ba). Their corresponding hydroxides are Be(OH)₂, Mg(OH)₂, Ca(OH)₂, Sr(OH)₂, and Ba(OH)₂.

**Hint**: Remember the group number and the metals that belong to it.

2. **Understand Solubility Trends**:
The solubility of alkaline earth metal hydroxides in water generally increases as we move down the group from beryllium to barium. This is due to the changes in lattice energy and hydration energy.

**Hint**: Lattice energy decreases and hydration energy remains relatively constant as you move down the group.

3. **Lattice Energy vs Hydration Energy**:
- **Lattice Energy**: The energy required to separate the ions in a solid ionic compound. It decreases down the group because the size of the metal ions increases, leading to weaker ionic bonds.
- **Hydration Energy**: The energy released when ions are surrounded by water molecules. This energy remains relatively constant for alkaline earth metals.

**Hint**: Consider how the size of the ions affects the energy interactions.

4. **Evaluate Each Hydroxide**:
- **Beryllium Hydroxide (Be(OH)₂)**: Least soluble due to high lattice energy.
- **Magnesium Hydroxide (Mg(OH)₂)**: More soluble than Be(OH)₂ but less than Ca(OH)₂.
- **Calcium Hydroxide (Ca(OH)₂)**: More soluble than Mg(OH)₂.
- **Strontium Hydroxide (Sr(OH)₂)**: Even more soluble than Ca(OH)₂.
- **Barium Hydroxide (Ba(OH)₂)**: Most soluble among these hydroxides.

**Hint**: Compare the solubility based on the position of the metal in the group.

5. **Conclusion**:
Based on the trends and evaluations, beryllium hydroxide (Be(OH)₂) is the least soluble alkaline earth metal hydroxide in water.

**Final Answer**: The least soluble alkaline earth metal hydroxide is **Beryllium Hydroxide (Be(OH)₂)**.